I use a low ohm meter (Kelvin), it's very good at
tracking down the nearest point of the short on the
board.
You may want to look at capacitors. Especially
tantalums, they short very nicely many times leaving
nothing but ash.





Sometimes it's possible to isolate sections of the circuit fairly easily, a
jumper link that can be removed, or in more drastic situations, a trace can
be cut. It doesn't take too many cycles of that to narrow things down.

Keep in mind that 5V TTL boards can pull quite a bit of juice, on larger
boards it can appear to be a nearly dead short when using an ohm meter
between Vcc and Gnd.